In a diesel engine, fuel is pressurized and supplied to a fuel rail via a high pressure pump and injected into a combustion chamber via a fuel injector. Under some circumstances, the high pressure pump is required to continuously provide fuel to the fuel rail in order to maintain a predetermined pressure in the fuel rail, and unused fuel will flow back into a fuel tank via a fuel return line from the high pressure pump. Operation of the high pressure pump may cause fuel pressure pulsation in the fuel return line, which may be excited to induce a vibration of the fuel line. In a vehicle with a diesel engine, a vibration of the fuel line may be transmitted into a vehicle body, thus causes a noise. A metallic pulsation damping box used in a conventional fuel line is expensive. Thus, there is a need for a simple and low cost fuel pressure pulsation damping device adapted for various fuel system.